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Q.11

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Found in: Page 525

### The Practice of Statistics for AP

Book edition 4th
Author(s) David Moore,Daren Starnes,Dan Yates
Pages 809 pages
ISBN 9781319113339

# The U.S. Forest Service is considering additional restrictions on the number of vehicles allowed to enter Yellowstone National Park. To assess public reaction, the service asks a random sample of 150 visitors if they favour the proposal. Of these, 89 say “Yes.”(a) Construct and interpret a 99% confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions.(b) Based on your work in part (a), can the U.S. Forest Service conclude that more than half of visitors to Yellow-stone National Park favour the proposal? Justify your answer.

a. the confidence interval is$\left(0.49,0.70\right)$

b. No

See the step by step solution

## step 1: introduction

Given, the service asks a random sample n =$150$

people who say yes x = $89$

Using,

$\stackrel{^}{p}-{z}_{\frac{a}{2}}×\sqrt{\frac{\stackrel{^}{p}×\left(1-\stackrel{^}{p}\right)}{n}}

$99%$confidence interval for the proportion of all visitors to Yellowstone who favours the restrictions is$\left(0.49,0.70\right)$

## step 2: explanation

From the above part, it is realized that the population extent is somewhere in the range of$0.49$and$0.70$. No, the U.S. Forest Service cant conclude that more than half of visitors to Yellow-stone National Park favour the proposal since the interval has the range $0.49$. Accordingly, it can't be inferred that the greater part of the guests are supportive of the proposition.